Transitivity Cannot Explain Perfect Syllogisms.

Abstract : Aristotle claims that the necessity of the syllogisms in the first figure is evident, and calls them “perfect” on this basis. The perfection of such syllogisms, most notably "barbara", appears to be correlated with the actual disposition of the middle term. G. Patzig strengthened the correlation to an explanation, claiming that in virtue of that disposition the transitivity of the relation “belongs to all” between the terms becomes manifest. The present article shows that the modern scheme of transitivity, namely, with contiguous middle term, is not the same as the one employed with remarkable consistency in the ancient mathematical texts. On these grounds, I argue that Patzig's calling into play the "notion" of transitivity cannot count as an explanation of first figure syllogisms being perfect, not even of those in "barbara".
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Submitted on : Thursday, April 29, 2010 - 12:09:24 PM
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Fabio Acerbi. Transitivity Cannot Explain Perfect Syllogisms.. Rhizai, 2009, 6, pp. 23-42. ⟨halshs-00477485⟩

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